Reaction Rate
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The reaction rate or rate of reaction is the speed at which a
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
takes place, defined as proportional to the increase in the
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
of a
product Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Produ ...
per unit time and to the decrease in the concentration of a
reactant In chemistry, a reagent ( ) or analytical reagent is a substance or compound added to a system to cause a chemical reaction, or test if one occurs. The terms ''reactant'' and ''reagent'' are often used interchangeably, but reactant specifies a ...
per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
under
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
is a slow reaction that can take many years, but the combustion of
cellulose Cellulose is an organic compound with the formula , a polysaccharide consisting of a linear chain of several hundred to many thousands of β(1→4) linked D-glucose units. Cellulose is an important structural component of the primary cell wall ...
in a fire is a reaction that takes place in fractions of a second. For most reactions, the rate decreases as the reaction proceeds. A reaction's rate can be determined by measuring the changes in concentration over time.
Chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in wh ...
is the part of
physical chemistry Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mecha ...
that concerns how rates of chemical reactions are measured and predicted, and how reaction-rate data can be used to deduce probable reaction mechanisms. The concepts of chemical kinetics are applied in many disciplines, such as
chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials int ...
,
enzymology Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. A ...
and
environmental engineering Environmental engineering is a professional engineering discipline that encompasses broad scientific topics like chemistry, biology, ecology, geology, hydraulics, hydrology, microbiology, and mathematics to create solutions that will protect and a ...
.


Formal definition

Consider a typical
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
: : + -> + The lowercase letters (''a'', ''b'', ''p'', and ''q'') represent
stoichiometric coefficients Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equals ...
, while the capital letters represent the
reactant In chemistry, a reagent ( ) or analytical reagent is a substance or compound added to a system to cause a chemical reaction, or test if one occurs. The terms ''reactant'' and ''reagent'' are often used interchangeably, but reactant specifies a ...
s (A and B) and the
products Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Produ ...
(P and Q). According to
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
's
Gold Book The International Union of Pure and Applied Chemistry publishes many books which contain its complete list of definitions. The definitions are divided into seven "colour books": Gold, Green, Blue, Purple, Orange, White, and Red. There is also an e ...
definition the reaction rate ''v'' for a chemical reaction occurring in a
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed. In ...
at
constant volume In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. ...
, without a build-up of
reaction intermediate In chemistry, a reaction intermediate or an intermediate is a molecular entity that is formed from the reactants (or preceding intermediates) but is consumed in further reactions in stepwise chemical reactions that contain multiple elementary st ...
s, is defined as: :v = - \frac \frac = - \frac \frac = \frac \frac = \frac \frac where denotes the
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
of the substance X (= A, B, P or Q). The reaction rate thus defined has the units of mol/L/s. The rate of a reaction is always positive. A
negative sign The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents subtraction, resul ...
is present to indicate that the reactant concentration is decreasing. The IUPAC recommends that the unit of time should always be the second. The rate of reaction differs from the rate of increase of concentration of a product P by a constant factor (the reciprocal of its stoichiometric number) and for a reactant A by minus the reciprocal of the stoichiometric number. The stoichiometric numbers are included so that the defined rate is independent of which reactant or product species is chosen for measurement. For example, if ''a = 1'' and ''b = 3'' then B is consumed three times more rapidly than A, but v ''= -d 'A''dt = -(1/3)d 'B''dt'' is uniquely defined. An additional advantage of this definition is that for an
elementary Elementary may refer to: Arts, entertainment, and media Music * ''Elementary'' (Cindy Morgan album), 2001 * ''Elementary'' (The End album), 2007 * ''Elementary'', a Melvin "Wah-Wah Watson" Ragin album, 1977 Other uses in arts, entertainment, a ...
and irreversible reaction, ''v'' is equal to the product of the probability of overcoming the
transition state In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
and the number of times per second the transition state is approached by reactant molecules. When so defined, for an elementary and irreversible reaction, ''v'' is the rate of successful chemical reaction events leading to the product. The above definition is only valid for a ''single reaction'', in a ''
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed. In ...
'' of ''constant volume''. If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction. For an open system, the full
mass balance In physics, a mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have b ...
must be taken into account: :F_ - F_\mathrm + \int_^ v\, dV = \frac, where ''F''A0 is the inflow rate of A in molecules per second, ''F''A the outflow, and ''v'' is the instantaneous reaction rate of A (in
number concentration A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
rather than molar) in a given differential volume, integrated over the entire system volume ''V'' at a given moment. When applied to the closed system at constant volume considered previously, this equation reduces to: :v= \frac, where the concentration is related to the number of molecules ''N''A by nbsp;= . Here ''N''0 is the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining con ...
. For a single reaction in a closed system of varying volume the so-called ''rate of conversion'' can be used, in order to avoid handling concentrations. It is defined as the derivative of the
extent of reaction In physical chemistry and chemical engineering, extent of reaction is a quantity that measures the extent to which the reaction has proceeded. Often, it refers specifically to the value of the extent of reaction when equilibrium has been reached. It ...
with respect to time. :v =\frac = \frac \frac = \frac \frac = \frac \left(V\frac + C_i \frac \right) Here ''νi'' is the stoichiometric coefficient for substance ''i'', equal to ''a'', ''b'', ''p'', and ''q'' in the typical reaction above. Also ''V'' is the volume of reaction and ''Ci'' is the concentration of substance ''i''. When side products or reaction intermediates are formed, the IUPAC recommends the use of the terms the rate of increase of concentration and rate of the decrease of concentration for products and reactants, properly. Reaction rates may also be defined on a basis that is not the volume of the reactor. When a
catalyst Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
is used the reaction rate may be stated on a catalyst weight (mol g−1 s−1) or surface area (mol m−2 s−1) basis. If the basis is a specific catalyst site that may be rigorously counted by a specified method, the rate is given in units of s−1 and is called a turnover frequency.


Influencing factors

Factors that influence the reaction rate are the nature of the reaction,
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
,
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
,
reaction order In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial react ...
,
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
,
solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
,
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
,
catalyst Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
,
isotopes Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers) ...
, surface area, stirring, and diffusion limit. Some reactions are naturally faster than others. The number of reacting species, their
physical state In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, ...
(the particles that form solids move much more slowly than those of gases or those in
solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...
), the complexity of the reaction and other factors can greatly influence the rate of a reaction. Reaction rate increases with concentration, as described by the
rate law In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial react ...
and explained by
collision theory Collision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the reactant hit each other with correct orientation, only a certain amount of collisions result in a percept ...
. As reactant concentration increases, the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of
collision In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great fo ...
increases. The rate of gaseous reactions increases with pressure, which is, in fact, equivalent to an increase in the concentration of the gas. The reaction rate increases in the direction where there are fewer moles of gas and decreases in the reverse direction. For condensed-phase reactions, the pressure dependence is weak. The order of the reaction controls how the reactant concentration (or pressure) affects the reaction rate. Usually conducting a reaction at a higher temperature delivers more energy into the system and increases the reaction rate by causing more collisions between particles, as explained by collision theory. However, the main reason that temperature increases the rate of reaction is that more of the colliding particles will have the necessary
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
resulting in more successful collisions (when bonds are formed between reactants). The influence of temperature is described by the
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1 ...
. For example, coal burns in a fireplace in the presence of oxygen, but it does not when it is stored at
room temperature Colloquially, "room temperature" is a range of air temperatures that most people prefer for indoor settings. It feels comfortable to a person when they are wearing typical indoor clothing. Human comfort can extend beyond this range depending on ...
. The reaction is spontaneous at low and high temperatures but at room temperature, its rate is so slow that it is negligible. The increase in temperature, as created by a match, allows the reaction to start and then it heats itself because it is exothermic. That is valid for many other fuels, such as
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Eart ...
,
butane Butane () or ''n''-butane is an alkane with the formula C4H10. Butane is a gas at room temperature and atmospheric pressure. Butane is a highly flammable, colorless, easily liquefied gas that quickly vaporizes at room temperature. The name but ...
, and
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
. Reaction rates can be independent of temperature (''non-Arrhenius'') or decrease with increasing temperature (''anti-Arrhenius''). Reactions without an activation barrier (for example, some radical reactions), tend to have anti-Arrhenius temperature dependence: the rate constant decreases with increasing temperature. Many reactions take place in solution and the properties of the solvent affect the reaction rate. The ionic strength also has an effect on the reaction rate. Electromagnetic radiation is a form of energy. As such, it may speed up the rate or even make a reaction spontaneous as it provides the particles of the reactants with more energy. This energy is in one way or another stored in the reacting particles (it may break bonds, and promote molecules to electronically or vibrationally excited states...) creating intermediate species that react easily. As the intensity of light increases, the particles absorb more energy and hence the rate of reaction increases. For example, when
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Eart ...
reacts with
chlorine Chlorine is a chemical element with the Symbol (chemistry), symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate betwee ...
in the dark, the reaction rate is slow. It can be sped up when the
mixture In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the ...
is put under diffused light. In bright sunlight, the reaction is explosive. The presence of a catalyst increases the reaction rate (in both the forward and reverse reactions) by providing an alternative pathway with a lower
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
. For example,
platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Platinu ...
catalyzes the combustion of hydrogen with oxygen at room temperature. The
kinetic isotope effect In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for th ...
consists of a different reaction rate for the same molecule if it has different isotopes, usually
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
isotopes, because of the relative mass difference between hydrogen and
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
. In
reactions on surfaces Reactions on surfaces are reactions in which at least one of the steps of the reaction mechanism is the adsorption of one or more reactants. The mechanisms for these reactions, and the rate equations are of extreme importance for heterogeneous c ...
, which take place for example during
heterogeneous catalysis In chemistry, heterogeneous catalysis is catalysis where the phase of catalysts differs from that of the reactants or products. The process contrasts with homogeneous catalysis where the reactants, products and catalyst exist in the same phase. ...
, the rate of reaction increases as the surface area does. That is because more particles of the solid are exposed and can be hit by reactant molecules. Stirring can have a strong effect on the rate of reaction for heterogeneous reactions. Some reactions are limited by diffusion. All the factors that affect a reaction rate, except for concentration and reaction order, are taken into account in the reaction
rate coefficient In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction. For a reaction between reactants A and B to form product C the reaction rate is often found to have the f ...
(the coefficient in the rate equation of the reaction).


Rate equation

For a
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
''a'' A + ''b'' B → ''p'' P + ''q'' Q, the rate equation or rate law is a
mathematical expression In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers ( constants), variables, operations, f ...
used in chemical kinetics to link the rate of a reaction to the
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
of each reactant. For a closed system at constant volume, this is often of the form :\,v = k mathrm mathrm - k_r mathrm mathrm For reactions that go to completion (which implies very small ''k''r), or if only the initial rate is analyzed (with initial vanishing product concentrations), this simplifies to the commonly quoted form :\,v = k(T) mathrm mathrm For gas phase reaction the rate equation is often alternatively expressed in terms of
partial pressure In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas ...
s. In these equations ''k''(''T'') is the ''reaction rate coefficient'' or ''rate constant'', although it is not really a constant, because it includes all the parameters that affect reaction rate, except for time and concentration. Of all the parameters influencing reaction rates, temperature is normally the most important one and is accounted for by the
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1 ...
. The exponents ''n'' and ''m'' are called reaction
orders Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of d ...
and depend on the reaction mechanism. For an elementary (single-step) reaction, the order with respect to each reactant is equal to its stoichiometric coefficient. For complex (multistep) reactions, however, this is often not true and the rate equation is determined by the detailed mechanism, as illustrated below for the reaction of H2 and NO. For elementary reactions or reaction steps, the order and stoichiometric coefficient are both equal to the
molecularity In chemistry, molecularity is the number of molecules that come together to react in an elementary (single-step) reactionAtkins, P.; de Paula, J. Physical Chemistry. Oxford University Press, 2014 and is equal to the sum of stoichiometric coeffici ...
or number of molecules participating. For a unimolecular reaction or step, the rate is proportional to the concentration of molecules of reactant, so the rate law is first order. For a bimolecular reaction or step, the number of collisions is proportional to the product of the two reactant concentrations, or second order. A termolecular step is predicted to be third order, but also very slow as simultaneous collisions of three molecules are rare. By using the
mass balance In physics, a mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have b ...
for the system in which the reaction occurs, an expression for the rate of change in concentration can be derived. For a closed system with constant volume, such an expression can look like :\frac = k(T) mathrm mathrm


Example of a complex reaction: hydrogen and nitric oxide

For the reaction :2H2(g) + 2NO(g) -> N2(g) + 2H2O(g) the observed rate equation (or rate expression) is: v = k ce ce2 \, As for many reactions, the experimental rate equation does not simply reflect the stoichiometric coefficients in the overall reaction: It is third order overall: first order in H2 and second order in NO, even though the stoichiometric coefficients of both reactants are equal to 2. In chemical kinetics, the overall reaction rate is often explained using a mechanism consisting of a number of elementary steps. Not all of these steps affect the rate of reaction; normally the slowest elementary step controls the reaction rate. For this example, a possible mechanism is: # \quad 2NO(g) <=> N2O2(g) \qquad(fast\ equilibrium) # \quad + H2 -> + H2O \qquad(slow) # \quad + H2 -> + H2O\qquad(fast) Reactions 1 and 3 are very rapid compared to the second, so the slow reaction 2 is the rate-determining step. This is a
bimolecular In chemistry, molecularity is the number of molecules that come together to react in an elementary (single-step) reactionAtkins, P.; de Paula, J. Physical Chemistry. Oxford University Press, 2014 and is equal to the sum of stoichiometric coeffici ...
elementary reaction whose rate is given by the second-order equation: : v = k_2 ce ce\,, where ''k''2 is the rate constant for the second step. However N2O2 is an unstable intermediate whose concentration is determined by the fact that the first step is in equilibrium, so that , where ''K''1 is the
equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
of the first step. Substitution of this equation in the previous equation leads to a rate equation expressed in terms of the original reactants : v = k_2 K_1 ce ce2 \, This agrees with the form of the observed rate equation if it is assumed that . In practice the rate equation is used to suggest possible mechanisms which predict a rate equation in agreement with experiment. The second molecule of H2 does not appear in the rate equation because it reacts in the third step, which is a rapid step ''after'' the rate-determining step, so that it does not affect the overall reaction rate.


Temperature dependence

Each reaction rate coefficient ''k'' has a temperature dependency, which is usually given by the
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1 ...
: : k = A e^. ''E''a is the
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
; ''R'' is the
gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
. Since at
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
''T'' the molecules have energies given by a
Boltzmann distribution In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability th ...
, one can expect the number of collisions with energy greater than ''Ea'' to be proportional to e. The coefficient, ''A'', is the pre-exponential factor or frequency factor. The values for ''A'' and ''E''a are dependent on the reaction. There are also more complex equations possible, which describe the temperature dependence of other rate constants that do not follow this pattern. Temperature is a measure of the average kinetic energy of the reactants. As temperature increases, the kinetic energy of the reactants increases. That is, the particles move faster. With the reactants moving faster this allows more collisions to take place at a greater speed, so the chance of reactants forming into products increases, which in turn results in the rate of reaction increasing. A rise of ten degrees Celsius results in approximately twice the reaction rate. The minimum kinetic energy required for a reaction to occur is called the activation energy and is denoted by ''E''a or ΔG. The transition state or activated complex shown on the diagram is the energy barrier that must be overcome when changing reactants into products. The molecules with an energy greater than this barrier have enough energy to react. For a successful collision to take place, the collision geometry must be right, meaning the reactant molecules must face the right way so the activated complex can be formed. A chemical reaction takes place only when the reacting particles collide. However, not all collisions are effective in causing the reaction. Products are formed only when the colliding particles possess a certain minimum energy called threshold energy. As a
rule of thumb In English, the phrase ''rule of thumb'' refers to an approximate method for doing something, based on practical experience rather than theory. This usage of the phrase can be traced back to the 17th century and has been associated with various t ...
, reaction rates for many reactions double for every ten degrees Celsius increase in temperature. For a given reaction, the ratio of its rate constant at a higher temperature to its rate constant at a lower temperature is known as its
temperature coefficient A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property ''R'' that changes when the temperature changes by ''dT'', the temperature coefficient α is def ...
, (''Q''). ''Q''10 is commonly used as the ratio of rate constants that are ten degrees Celsius apart.


Pressure dependence

The pressure dependence of the rate constant for condensed-phase reactions (that is, when reactants and products are solids or liquid) is usually sufficiently weak in the range of pressures normally encountered in industry that it is neglected in practice. The pressure dependence of the rate constant is associated with the activation volume. For the reaction proceeding through an activation-state complex: :A + B , A⋯B, → P the activation volume, Δ''V'', is: :\Delta V^ = \bar_ - \bar_\mathrm - \bar_\mathrm where ''V̄'' denotes the
partial molar volume In thermodynamics, a partial molar property is a quantity which describes the variation of an extensive property of a solution or mixture with changes in the molar composition of the mixture at constant temperature and pressure. It is the p ...
of a species and ‡ indicates the activation-state complex. For the above reaction, one can expect the change of the
reaction rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction. For a reaction between reactants A and B to form product C the reaction rate is often found to have the ...
(based either on
mole fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ex ...
or on
molar concentration Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
) with pressure at constant temperature to be: : \left(\frac \right)_T = -\frac In practice, the matter can be complicated because the partial molar volumes and the activation volume can themselves be a function of pressure. Reactions can increase or decrease their rates with pressure, depending on the value of Δ''V''. As an example of the possible magnitude of the pressure effect, some organic reactions were shown to double the reaction rate when the pressure was increased from atmospheric (0.1 MPa) to 50 MPa (which gives Δ''V'' = −0.025 L/mol).


See also

*
Rate of solution In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...
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Dilution (equation) Dilution is the process of decreasing the concentration of a solute in a solution, usually simply by mixing with more solvent like adding more water to the solution. To dilute a solution means to add more solvent without the addition of more sol ...
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Diffusion-controlled reaction Diffusion-controlled (or diffusion-limited) reactions are reactions in which the reaction rate is equal to the rate of transport of the reactants through the reaction medium (usually a solution). The process of chemical reaction can be considered ...
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Steady state approximation In chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, ...
* Collision theory and
transition state In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
are chemical theories that attempt to predict and explain reaction rates. *
Isothermal microcalorimetry Isothermal microcalorimetry (IMC) is a laboratory method for real-time monitoring and dynamic analysis of chemical, physical and biological processes. Over a period of hours or days, IMC determines the onset, rate, extent and energetics of such pr ...


Notes


External links


Chemical kinetics, reaction rate, and order
(needs flash player)

(lecture with audio).



* ttp://www.nrcresearchpress.com/doi/pdf/10.1139/v66-330 pressure dependence Can. J. Chem.] {{DEFAULTSORT:Reaction Rate Chemical kinetics Chemical reaction engineering Temporal rates